Over the last thirty years, computer tomography (CT) has gone from image reconstruction based on scanning in a slice-by-slice process to spiral scanning to also include non-spiral scanning techniques such as those performed with C-arm devices, with all techniques and devices experiencing problems with image reconstruction.
From the 1970s to 1980s the slice-by-slice scanning was used. In this mode the incremental motions of the patient on the table through the gantry and the gantry rotations were performed one after another. Since the patient was stationary during the gantry rotations, the trajectory of the x-ray source around the patient was circular. Pre-selected slices through the patient were reconstructed using the data obtained by such circular scans.
From the mid 1980s to present day, spiral type scanning has become the preferred process for data collection in CT. Under spiral scanning a table with the patient continuously moves at a constant speed through the gantry that is continuously rotating about the table. At first, spiral scanning has used one-dimensional detectors, which receive data in one dimension (a single row of detectors). Later, two-dimensional detectors, where multiple rows (two or more rows) of detectors sit next to one another, have been introduced. In CT there have been significant problems for image reconstruction especially for two-dimensional detectors. Data provided by the two-dimensional detectors will be referred to as cone-beam (CB) data or CB projections.
In addition to spiral scans there are non-spiral scans, in which the trajectory of the x-ray source is different from spiral. In medical imaging, non-spiral scans are frequently performed using a C-arm device, which is usually smaller and more portable than spiral type scanning systems. For example, C-arm scanning devices have been useful for being moved in and out of operating rooms, and the like.
FIG. 1 shows a typical prior art arrangement of a patient on a table that moves through a C-arm device, that is capable of rotating around the patient, having an x-ray tube source and a detector array, where cone beam projection data sets are received by the x-ray detector, and an image reconstruction process takes place in a computer with a display for the reconstructed image.
There are known problems with using C-arm devices to reconstruct images. See in particular for example, pages 755-759 of Kudo, Hiroyuki et al., Fast and Stable Cone-Beam Filtered Back projection Method for Non-planar Orbits, IOP Publishing LTD, 1998, pp. 747-760. The Kudo paper describes image reconstruction using C-arm devices for various shift-variant filtered back projection (FBP) structures, which are less efficient than convolution-based FBP algorithms.
For three-dimensional, also known as volumetric, image reconstruction from the data provided by spiral and non-spiral scans with two-dimensional detectors, there are two known groups of algorithms: Exact algorithms and Approximate algorithms, that each have known problems. Under ideal circumstances, exact algorithms can provide a replication of an exact image. Thus, one should expect that exact algorithms would produce images of good quality even under non-ideal (that is, realistic) circumstances.
However, exact algorithms can be known to take many hours to provide an image reconstruction, and can take up great amounts of computer power when being used. These algorithms can require keeping considerable amounts of cone beam projections in memory. Some other exact algorithms are efficient, but may require excessive amounts of CB data, which results in an increased x-ray dose to the patient.
Approximate algorithms possess a filtered back projection (FBP) structure, so they can produce an image very efficiently and using less computing power than Exact algorithms. However, even under the ideal circumstances these algorithms produce an approximate image that may be similar to but still different from the exact image. In particular, approximate algorithms can create artifacts, which are false features in an image. Under certain circumstances and conditions these artifacts could be quite severe.
To date, there are no known algorithms that can combine the beneficial attributes of exact and approximate algorithms into a single algorithm that is capable of replicating an exact image under the ideal circumstances, uses small amount of computer power, requires minimal amount of CB data, and reconstructs the exact images in an efficient manner (i.e., using the FBP structure) in the cases of general circle-plus trajectories.
Hereinafter the phrase that “the process of the present invention reconstructs an exact image” means that the process is capable of reconstructing an exact image. Since in real life any data contains noise and other imperfections, no algorithm is capable of reconstructing an exact image.
Image reconstruction has been proposed in many U.S. Patents. See for example, U.S. Pat. Nos. 5,663,995 and 5,706,325 and 5,784,481 and 6,014,419 to Hu; 5,881,123 and 5,926,521 and 6,130,930 and 6,233,303 and 6,292,525 to Tam; 5,960,055 to Samaresekera et al.; 5,995,580 to Schaller; 6,009,142 to Sauer; 6,072,851 to Sivers; 6,173,032 to Besson; 6,198,789 to Dafni; 6,215,841 and 6,266,388 to Hsieh. Other U.S. patents have also been proposed for image reconstruction as well. See U.S. Pat. Nos. 6,504,892 to Ning; 6,148,056 to Lin; 5,784,481 to Hu; 5,706,325 to Hu; and 5,170,439 to Zeng et al.
Mathematically, the problem of image reconstruction in computer tomography (CT) consists of finding an unknown function ƒ(x), x∈P3, from its integrals along lines that intersect a curve. The curve is called the source trajectory, and the collection of line integrals is called the cone beam data. A typical CT scanner consists of two major parts: a gantry and patient table. The gantry is a doughnut-shaped device, where an x-ray source and x-ray detector are located opposite each other. The patient lies on the table, which is then inserted into the rotating gantry. By transmitting x-rays through the patient the cone beam data are collected. By varying the motion of the table through the gantry one obtains different source trajectories. To simplify mathematics, one usually assumes that the patient is stationary, and the gantry moves relative to the patient.
Cardiac and, more generally, dynamic imaging is a very important challenge for modern tomography. Circle is usually the most convenient trajectory. As opposed to helix, in a circular scan the gantry does not move away from the dynamically changing region of interest. As opposed to the helix, in the circular scan the gantry does not move away from the dynamically changing region of interest (ROI). As opposed to a saddle trajectory, the circular scan does not involve moving the patient back and forth, which can be uncomfortable. The major disadvantage of the circular trajectory is its incompleteness. For this reason a pure circular scan is complemented by an additional trajectory, such as a line, arc, helical segment, etc., which makes it complete. So the problem of developing a reconstruction algorithm for such trajectories is of significant practical interest.
Theoretically exact and efficient filtered back projection (FBP) algorithms have been developed for a number of specific circle-plus trajectories, such as circle+line described in Image reconstruction for the circle and line trajectory, Physics in Medicine and Biology, 2004, pp. 5059-5072, vol. 49, circle+arc described in Image reconstruction for the circle and arc trajectory, Physics in Medicine and Biology, 2005, pp. 2249-2265, vol. 50; G. H. Chen, T. L. Zhuang, S. Leng, and B. E. Nett, Shift-invariant and mathematically exact cone-beam FBP reconstruction using a factorized weighting function, IEEE Transactions on Medical Imaging, 2006, circle+helical segment described in C. Bontus, P. Koken, Th. Köhler, R. Proksa, Circular CT in combination with a helical segment, Physics in Medicine and Biology, 2007, pp. 107-120, vol. 51.
A very nice exact FBP algorithm was recently proposed by J. D. Pack, F. Noo. R. Clackdoyle, Cone-beam reconstruction using the back-projection of locally filtered projections, IEEE Transactions on Medical Imaging, 2005, pp. 1-16, vol. 24. It applies to almost any source trajectory, but sometimes leads to excessive detector requirements. The problem is that the algorithm is too general and does not take the geometry of the curve into account.
Back projection-filtration (BPF) algorithms are very flexible and can be easily derived for almost any scanning curve described in T. Zhuang, S. Leng, B. E. Nett, G. Chen, Fan-beam and cone-beam image reconstruction via filtering the backprojection image of differentiated projection data, Physics in Medicine and Biology, 2004, pp. 1643-1657, vol. 49; J. D. Pack, F. Noo, Cone-beam reconstruction using 1D filtering along the projection of M-lines, Inverse Problems, 2005, pp. 1105-1120, vol. 21; J. D. Pack, F. Noo, R. Clackdoyle, Cone-beam reconstruction using the back-projection of locally filtered projections, IEEE Transactions on Medical Imaging, 2005, pp. 1-16, vol. 24; Y. Zou, X. Pan, D. Xia, G. Wang, PI-line-based image reconstruction in helical cone-beam computed tomography with a variable pitch, Medical Physics, 2005, pp. 2639-2648, vol. 32; E. Y. Sidky, Y. Zou, X. Pan, Minimum data image reconstruction algorithms with shift-invariant filtering for helical, cone-beam CT, Physics in Medicine and Biology, 2000, pp. 91-100, vol. 11; H. Yu, S. Zhao, Y. Ye, G. Wang, Exact BPF and FBP algorithms for nonstandard saddle curves, Medical Physics, 2005, pp. 3305-3312, vol. 32; Y. Ye. S. Zhao, H. Yu, G. Wang, A general exact reconstruction for cone-beam CT via backprojection-filtration, IEEE Transactions on Medical Imaging, 2005, pp. 1190-1198, vol. 24; T. Zhuang, G. H. Chen, New families of exact fan-beam and cone-beam image reconstruction formulae via filtering the back projection image of differentiated projection data along singly measured lines, Inverse Problems, 2006, pp. 991-1006, vol. 22, but they are generally less efficient than their FBP counterparts.
The problem to be solved is the development of a reconstruction algorithm for such trajectories, such as circle+line, circle+arc, circle+helical segments and almost any continuous curve C plus an additional curve L under the condition that L starts below or on C and ends above C. Back projection-filtration algorithms are very flexible and can be easily derived for almost any scanning curve, but they are generally less efficient than their filtered back projection counterparts.
What is needed is a reconstruction algorithm for almost any continuous curve C plus an additional curve L under the condition that L starts below or on C and ends above C implemented using shift-invariant filtered back projection with only a few one-dimensional families of filtering lines.